Building ML to finding the closest matching image based on users drawing
There is a good project you can research to find information on this specific task, it is Google quickdraw. It has 50 million drawings across 345 categories and it was used in Google autoDraw. AutoDraw guesses what you’re trying to draw.

You can use quickdraw dataset to train a neural network (Sequence-to-Sequence Variational Autoencoder) in order to get draws from your Sketches. for more info on this read this papper

Classified Sketches into categories is a difficult task because Sketches are a high-level representation that does not always convey enough information to distinguish between different categories.

The the best approach will depend on your specific needs